1. (Here you should interpret the “mod 2” as describing an operation to each element of the output vector.) For example, [1, 1, 1, 1] · G = [1, 1, 1, 1, 3, 3, 3], so we’d encode [1, 1, 1, 1] as [1, 1,...

1. (Here you should interpret the “mod 2” as describing an operation to each element of the output vector.) For example, [1, 1, 1, 1] · G = [1, 1, 1, 1, 3, 3, 3], so we’d encode [1, 1, 1, 1] as [1, 1, 1, 1, 3, 3, 3] mod 2 = [1, 1, 1, 1, 1, 1, 1]. What is the Hamming code encoding of the following messages?

1. [0, 0, 0, 0]

2. [0, 1, 1, 0]

3. [1, 0, 0, 1]

2. Consider the function f : {0, 1, . . . 7} → {0, 1, . . . 7} defined by f(x) := (x
²
+ 3) mod 8